The Logics of Strict-Tolerant Logic

Abstract

Adding a transparent truth predicate to a language completely governed by classical logic is not possible. The trouble, as is well-known, comes from paradoxes such as the Liar and Curry. Recently, Cobreros, Egré, Ripley and van Rooij have put forward an approach based on a non-transitive notion of consequence which is suitable to deal with semantic paradoxes while having a transparent truth predicate together with classical logic. Nevertheless, there are some interesting issues concerning the set of metainferences validated by this logic. In this paper, we show that this logic, once it is adequately understood, is weaker than classical logic. Moreover, the logic is in a way similar to the paraconsistent logic LP.

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Acknowledgments

We owe thanks to Norbert Gratzl, Ole Hjortland, Francesco Paoli, Lavinia Picollo, Dave Ripley, Thomas Schindler, and Johannes Stern for very helpful comments on previous versions of this paper. Some of this material was presented at conferences in Barcelona (Logos), Munich (MCMP) and Buenos Aires (Buenos Aires Logic Group). We are very grateful to the members of these audiences for their valuable feedback. We are also specially grateful to Jose Martinez and Elia Zardini for organizing the Substructural Approaches to Paradox Workshop and to Thomas Meier for organizing the 1st MCMP Munich-Buenos Aires Workshop.